Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
def isTriangle(n):
	a = math.sqrt(2*n)
	b = math.floor(a)
	if b*(b+1) == 2*n:
		return True
	else:
		return False

def Triangle(m):
	return (m*(m+1))//2

N = int(input())
t = 0
for i in range(1,int(math.sqrt(N))+1):
	a = Triangle(i)
	b = N - a
	if b>0 and isTriangle(b):
		print("YES")
		t = 1
		break
if t == 0:
	print("NO")